ISI ME-1 2011

[AS]

17. The value of the function f (x)=x+integral(xy^2+ x^2y)f(y)dy from (0-1)
is px + qx^2 , where
(a) p = 80, q = 180,
(b) p = 40, q = 140
(c) p = 50, q = 150,
(d) None of these

[maahi]

its pretty easy . functional  form of f(y) is not specified so how will u integrate d function and hence d ans none .

[duck]

Hi.. :)

The reason why its option(d) is not what "Maahi" has specified.
Its given that f(x) = px+qx^2.
So, you can write f(y) = py+qy^2.
Now, just put this f(y) in the integral and integrate.
You'll get p=180/119 and q=80/119

[maahi]

ooh thanks